Definition:Nondegenerate Subspace of Scalar Product Space

Definition

Let $\struct {V, q}$ be a scalar product space.

Let $S \subseteq V$ be a subspace.

Suppose the restriction of $q$ to $S \times S$ is nondegenerate, where $\times$ denotes the cartesian product.

Then $S$ is said to be nondegenerate.

Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Pseudo-Riemannian Metrics